Research On Bifurcations And Chaos In Voltage-Fed DC-DC Converter

As a kind of typical piecewise smooth nonlinear systems, DC-DC switching converter contains abundant nonlinear phenomena, such as bifurcations and chaos, when working under some parameter conditions. The nonlinear phenomena may cause the high-frequency noise, sudden collapse of critical operation and other unpredictable malfunctions in the converter. And that would lead to some irreversible harm when the system was operating in the stable state. With the rapid development of power electronics technology, the systems supported by switching power supply require that the converter must have better stability and reliability. Therefore, it is of great practical significance to understand the essence of nonlinear phenomena in DC-DC switching converter deeply so as to avoid such irregular phenomena efficiently when the practitioners design the converter. Through the bifurcation diagram, phase trajectory and time-domain waveform, this paper studies nonlinear phenomena in a typical non-isolated switching converter and a typical isolated switching converter, respectively.First, the thesis studies the dynamic characteristic of Buck-Boost converter----a kind of typical non-isolated switching converter. According to the basic working principle of the Buck-Boost converter operating under discontinuous conduction mode, we derive its precise discrete iterative map and it provides a reliable mathematical basis for further study. Subsequently, based on the precise discrete iterative map and the piecewise linear model, through using the Matlab to simulate the converter numerically, we obtained the bifurcation diagram relying the feedback coefficient, the time-domain waveform diagram and the phase trajectory diagram at corresponding typical feedback coefficients. Through the analytical result of the converter, we can determine the stability domain of periodic orbits. And that provides advice for switching power supply development engineers.Second, this paper studies the dynamic characteristic of Flyback converter----a kind of typical isolated switching converter. Introducing the concept of ampere-turns when establishing its precise discrete iterative map so that the maturity method that analyzing the non-isolated converter circuit only can be applied to analyze the Flyback converter directly. Based on the precise discrete iterative map of the Flyback converter, we can obtain the bifurcation diagram in connection with the feedback coefficient. Finally, through numerical simulation and analog simulation, the validity of the model can be verified.Lastly, by combining Filippov’s method and the Floquet theory, the author studies the evolution of perturbations about a nominal periodic orbit of Buck-Boost converter in discontinuous conduction mode and achieves analyzing the orbital stability.